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(a) Use the fundamental matrix method, identify what the matrices Q and R are. Find (IQ)-¹ and (IQ)-¹R. (b) Use the results from part (a) to find the probability that a newly hired junior lawyer will eventually leave the firm before becoming a partner. (c) On average, how many years a junior lawyer stays in the firm as a senior lawyer before he/she finally leaves the company (either as a partner or not)? (d) On average, how long does a newly hired junior lawyer stay with the firm?

(a) Use the fundamental matrix method, identify what the matrices Q and R are. Find (IQ)-¹ and (IQ)-¹R. (b) Use the results from part (a) to find the probability that a newly hired junior lawyer will eventually leave the firm before becoming a partner. (c) On average, how many years a junior lawyer stays in the firm as a senior lawyer before he/she finally leaves the company (either as a partner or not)? (d) On average, how long does a newly hired junior lawyer stay with the firm?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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9. A law firm employs three types of lawyers: junior lawyers, senior lawyers, and partners. During a given year, there is a 0.1 probability that a junior lawyer will be promoted to senior lawyer and a 0.05 probability that he or she will leave the firm. Also, there is a 0.2 probability that a senior lawyer will be promoted to partner and a 0.15 probability that he or she will leave the firm. There is a 0.03 probability that a partner will leave the firm. The firm never demotes a lawyer. th Let Xn be the status of an employee at the n' year after he or she has been hired, it could be one of the three types of lawyers (junior, senior, or partner) or two types of leaving (either leaving as a partner or leaving as a non-partner). Let state 0-junior, state 1-senior, state 2=partner, state 3= leave as non-partner, state 4= leave as partner The (one-step) transition matrix is P = 0.85 0 0 0 0 0.1 0 0.05 0.65 0.2 0.15 0 0.97 0 0 1 0 0 0 0 0 0 0.03 0 1 (a) Use the fundamental matrix method, identify what the matrices Q and R are. Find (I — Q)−¹ and (I — Q)¯¹R. (b) Use the results from part (a) to find the probability that a newly hired junior lawyer will eventually leave the firm before becoming a partner. (c) On average, how many years a junior lawyer stays in the firm as a senior lawyer before he/she finally leaves the company (either as a partner or not)? (d) On average, how long does a newly hired junior lawyer stay with the firm?
Transcribed Image Text:9. A law firm employs three types of lawyers: junior lawyers, senior lawyers, and partners. During a given year, there is a 0.1 probability that a junior lawyer will be promoted to senior lawyer and a 0.05 probability that he or she will leave the firm. Also, there is a 0.2 probability that a senior lawyer will be promoted to partner and a 0.15 probability that he or she will leave the firm. There is a 0.03 probability that a partner will leave the firm. The firm never demotes a lawyer. th Let Xn be the status of an employee at the n' year after he or she has been hired, it could be one of the three types of lawyers (junior, senior, or partner) or two types of leaving (either leaving as a partner or leaving as a non-partner). Let state 0-junior, state 1-senior, state 2=partner, state 3= leave as non-partner, state 4= leave as partner The (one-step) transition matrix is P = 0.85 0 0 0 0 0.1 0 0.05 0.65 0.2 0.15 0 0.97 0 0 1 0 0 0 0 0 0 0.03 0 1 (a) Use the fundamental matrix method, identify what the matrices Q and R are. Find (I — Q)−¹ and (I — Q)¯¹R. (b) Use the results from part (a) to find the probability that a newly hired junior lawyer will eventually leave the firm before becoming a partner. (c) On average, how many years a junior lawyer stays in the firm as a senior lawyer before he/she finally leaves the company (either as a partner or not)? (d) On average, how long does a newly hired junior lawyer stay with the firm?
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